Ethylene-α-olefin-unconjugated diene random copolymers are widely used as automobile materials, construction materials, industrial materials, electric wire materials and the like because they are excellent in properties such as heat resistance, weathering resistance and ozone resistance, and they have been produced using vanadium catalysts. However, these catalysts suffer from the problems that catalytic efficiency (polymer production per unit vanadium catalyst) is low, a large cost is required, and further the catalytic efficiency sharply reduces at high temperatures, and hence polymerization at high temperatures is difficult and a relatively high cost is required for post-treatments.
On the other hand, recently, investigation on the production of the copolymer using a metallocene catalyst system comprising aluminoxane which is capable of performing the polymerization at high temperatures, but the metallocene catalyst system has a problem that the molecular weight of the resulting copolymer is low (JP-A-58-19309, U.S. Pat. No. 4,542,199). There is another metallocene catalyst system comprising an alkylaluminum compound and a boron compound (JP-A-3-207704, U.S. Pat. No. 5,519,100). However, the boron compound which can give a high catalytic efficiency is mostly solid, and in order to produce copolymers stably with a high catalytic efficiency, it is preferred to use an aromatic solvent in which a solid boron compound is highly soluble. In the case of using an aromatic solvent, the post-treatments require more troubles than using an aliphatic hydrocarbon solvent.